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Laurent Lafforgue was awarded the Fields Medal for his proof of the Langlands correspondence for the general linear groups GLr over function fields of positive characteristic. His approach to this problem follows the basic strategy introduced twenty-five years ago by V. Drinfeld in his proof for GL2. Already Drinfeld’s proof is extremely difficult. Lafforgue’s proof is a real tour de force, taking up as it does several hundred pages of highly condensed reasoning. By his achievement Lafforgue has proved himself a mathematician of remarkable strength and perseverance.

The Mathematical Work of the 2002 Fields Medalists